Quantum Predictive Filtering

Abstract

How can relevant information be extracted from a quantum process? In many situations, only some part of the total information content produced by an information source is useful. Can one then find an efficient encoding, in the sense of retaining the largest fraction of relevant information? This paper offers one possible solution by giving a generalization of a classical method designed to retain as much relevant information as possible in a lossy data compression. A key feature of the method is to introduce a second information source to define relevance. We quantify the advantage a quantum encoding has over the best classical encoding in general, and we demonstrate using examples that a substantial quantum advantage is possible. A main result, however, is that if the relevant information is purely classical, then a classical encoding is optimal.

References in corpus (7)

• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• On the quantum, classical and total amount of correlations in a quantum state
• Quantum information can be negative
• The thermodynamic meaning of negative entropy
• The thermodynamics of prediction
• Efficient computation of the Zassenhaus formula
• Quantum-to-classical rate distortion coding

Cited by in corpus (7)

• Convexity and Operational Interpretation of the Quantum Information Bottleneck Function
• Quantum Rate-Distortion Coding of Relevant Information
• Efficient algorithms for quantum information bottleneck
• Strong converse bounds in quantum network information theory: distributed hypothesis testing and source coding
• On the structure and convergence of the symmetric Zassenhaus formula
• Generalized quantum Arimoto-Blahut algorithm and its application to quantum information bottleneck
• On Improving the Performance of Nonphotochemical Quenching in CP29 Light-Harvesting Antenna Complex